Heisenberg-Weyl Observables: Bloch vectors in phase space

Author(s): A. Asadian, P. Erker, M. Huber, C. Kloeckl

Journal: Phys. Rev. A

Volume: 94

Year: 2016

DOI Number: 10.1103/PhysRevA.94.010301

Link: Link to publication

Abstract:

We introduce a Hermitian generalization of Pauli matrices to higher dimensions which is based on Heisenberg-Weyl operators. The complete set of Heisenberg-Weyl observables allows us to identify a real-valued Bloch vector for an arbitrary density operator in discrete phase space, with a smooth transition to infinite dimensions. Furthermore, we derive bounds on the sum of expectation values of any set of anticommuting observables. Such bounds can be used in entanglement detection and we show that Heisenberg-Weyl observables provide a first nontrivial example beyond the dichotomic case.